The theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling and derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity.
Abstract
Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant. To effectively leverage structural information embedded within the unlabeled dataset and compensate for sparse conditioning signals, we propose a semi-supervised framework combining conditional stochastic interpolation with low-dimensional latent representations. RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction. This isolates the supervised learning of conditional dependencies to a low-dimensional space, requiring few labels while utilizing the abundant unlabeled data purely for reconstruction. Theoretically, we establish an error decomposition showing that the Kullback-Leibler divergence of RepG comprises stage-wise estimation errors and a structural bias quantified by conditional mutual information. For deep neural network estimators, we derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity. By confining the supervised estimation burden to the low intrinsic dimension of the latent representation, RepG achieves a strictly faster convergence rate. Complemented by a minimax lower bound, our theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling.
Conditional diffusion models have become a powerful and flexible framework for learning complex conditional distributions from labeled data. In practice, however, acquiring high-quality labels is costly and time-consuming, leaving large volumes of unlabeled data unused. To address this, we introduce label-augmented conditional diffusion (LACD), a simple and effective approach that incorporates unlabeled examples by assigning them a designated trivial label and performing joint denoising score matching over the augmented dataset. We provide sufficient conditions guaranteeing population-level identifiability of the target conditional distribution under this scheme. Moreover, we establish rigorous statistical guarantees: when sufficiently many unlabeled samples are available, the sampling distribution produced by LACD converges strictly faster than the purely supervised estimator in total variation distance, and at least as fast in Wasserstein-1 distance. Extensive experiments on synthetic, image, and tabular benchmarks corroborate our theory and show substantial gains in sample efficiency and generative performance compared with the purely supervised estimator.
Jin Su, Yuan Gao, Yong Zhou et al.· arXiv.org· 0 citations
This work presents a framework for learning continuous latent representations of admissible partial differential equations by embedding a scientific inductive bias directly into the training distribution, and shows that embedding a scientific inductive bias in the training distribution enables the learning of compact and geometrically meaningful hypothesis manifolds.
James Crowley, Faez Ahmed, A. van Beek· 0 citations
Mixed-type data containing both numerical and categorical variables arise in many scientific and real-world applications. Existing representation learning and generative modeling approaches typically focus either on reconstruction accuracy or unconditional data generation, but often fail to recover the full conditional distribution of the data while preserving interpretable structural relationships between heterogeneous variable types. In this work, we introduce Conditional-Independence-Regularized Distributional Autoencoders, a framework for learning low-dimensional representations of mixed-type data through conditional distribution matching and structural regularization. Our method combines an energy-score-based objective for numerical variables, a likelihood-based objective for categorical variables, and an auxiliary conditional independence regularization term encouraging the learned representation to capture the dependence between numerical and categorical components. We provide theoretical analysis showing that the optimal representation balances unexplained numerical variability, conditional entropy of categorical variables, and residual conditional dependence. Empirically, the proposed method achieves strong performance on both synthetic and real-world datasets, substantially improving categorical distribution recovery, achieving competitive overall conditional distribution recovery, and preserving mixed-type dependence structure. The code has been made available at GitHub.
This work introduces a novel framework, Gaussian Bridge Consistency (GBC), to address challenges of semi-supervised learning by constructing semantic interpolation paths between unlabeled samples and high-quality class anchors, and proposes BridgeMix, a confidence-aware feature mixing strategy that interpolates both sample and anchor pairs to amplify cross-sample generalization.
Hong-Yang He, Xin-Yuan Song, Yan Zhong et al.· 0 citations
Gaussian-mixture calculations and a medical diagnosis example illustrate how uncertainty-dependent labeling mechanisms can improve estimation and classification under a fixed labeling budget.
You‐Gan Wang, Jinran Wu, Geoffrey J. McLachlan· 0 citations
A novel PML method, namely Wasserstein Partial Multi-Label Learning with dual Label Correlation Perspectives (Wpml3cp), solved by the gradient descent with an augmented Lagrange multiplier technique, and empirical results demonstrate that Wpml3cp and Wpml3cp-D can outperform the PML baselines in various noisy levels.
Ximing Li, Yuanchao Dai, Bing Wang et al.· ACM Transactions on Knowledg...· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
